1. Field of the Invention
The present invention relates to a method of processing multi-component seismic data. It particularly relates to a method of processing seismic data to determine a calibration filter that calibrates one component of the seismic data relative to another component of the seismic data The invention further relates to an apparatus for processing seismic data.
2. Description of the Related Art
FIG. 1 is a schematic view of a seismic surveying arrangement. In this figure the surveying arrangement is a marine surveying arrangement in which seismic energy is emitted by a seismic source 1 that is suspended within a water column 2 from a towing vessel 3. In this example the water column is the sea, but the methods described hereinbelow can be applied to data acquired in seawater or in freshwater. When the seismic source 1 is actuated seismic energy is emitted downwards and is detected by an array of seismic receivers 4 disposed on the seafloor 5. (As used herein the term “seabed” denotes the earth's interior, and the term “seafloor” denotes the surface of the seabed.)
Many seismic surveys now use multi-component receivers that record two or more components of the seismic energy incident on the receiver. For example a 3-component (3-C) seismic receiver contains three orthogonal geophones and so can record the x-, y- and z-components of the particle motion at the receiver (the particle motion may be the particle displacement, particle velocity or particle acceleration or even, in principle, a higher derivative of the particle displacement). In a marine seismic survey a 4-component (4-C) seismic receiver can alternatively be used. A 4-C receiver contains a (dynamic) pressure sensor such as a hydrophone in addition to three orthogonal geophones and so can record pressure fluctuations as acoustic waves propagate in the water column (a scalar quantity) in addition to the x-, y- and z-components of the particle motion of the seabed.
Many different paths exist by which seismic energy may travel from the source 1 to a receiver 4 in the seismic surveying arrangement of FIG. 1. A number of paths are indicated schematically in FIG. 1.
The path 6 shown in FIG. 1 is known as the “direct path”. Seismic energy that travels along the direct path 6 travels from the source 1 to a receiver 4 essentially in a straight line without undergoing reflection at any interface.
Path 7 in FIG. 1 is an example of a “water layer multiple path”. Seismic energy that follows a water layer multiple path propagates wholly within the water column 2, but undergoes one or more reflections at the surface of the water column and/or the seafloor 5 so that the seismic energy passes through the water column more than once. The water layer multiple path 7 shown in FIG. 1 involves one reflection at the seafloor 5 and one reflection at the surface of the water column, but many other water layer multiple paths exist.
The path 8 in FIG. 1 is an example of a “critical refraction path”. Seismic energy that follows the path 8 propagates downwards to the seafloor 5, and penetrates into the earth's interior 10 (ie into the seabed). The seismic energy continues propagating downwardly, until it reaches a boundary 11 between two layers of the earth that have different acoustic impedance. The seismic energy undergoes critical refraction, propagates along the boundary 11, before eventually being refracted upwards towards the receiver 4. Critical refraction may also occur at the water-seabed interface, and downwardly propagating seismic energy that is refracted in this way will propagate along the water-seabed interface and will then propagate upwardly into the water column.
The path 9 shown in FIG. 1 is known as a “primary reflection path”. Seismic energy that follows the primary reflection path 9 propagates downwards through the water column, is refracted at the seafloor 5, and propagates downwardly through the earth's interior. The seismic energy is refracted at the boundary 11, but is not critically refracted and so continues to propagate downwardly into the earth. It eventually undergoes reflection at a geological structure 12 that acts as a partial reflector of seismic energy, and the reflected seismic energy is, after further refraction as it passes upwardly through the boundary 11, incident on the receiver 4. The general intent of a seismic survey is to make use of the seismic energy that follows the primary reflection path in order to obtain information about the interior structure of the earth.
Seismic energy acquired at a receiver may contain upwardly and/or downwardly propagating seismic energy depending on the location of the receiver and on the event. For example seismic energy that travels along the critical refraction path 8 shown in FIG. 1 will, when it is incident (travelling upwardly) on the water-seabed interface, be partly transmitted into the water column and partially reflected back into the seabed 10. Thus, a critical refraction event will consist purely of upwardly propagating seismic energy above the seafloor 5, but will contain both upwardly and downwardly propagating seismic energy below the seafloor 5. As another example, seismic energy that travels along the direct path 6 shown in FIG. 1 will, when incident on the water-seabed interface 5, be partially transmitted into the seabed and partially reflected back into the water column. Hence, the direct event will contain both upwardly and downwardly propagating seismic energy above the seafloor, but will contain only downwardly propagating seismic energy below the seafloor. It is therefore often of interest to decompose the seismic data acquired at the receiver 4 into an up-going constituent and a down-going constituent, above or below the seafloor 5. For example, in a 4-C seismic survey it may be of interest to decompose the pressure and the vertical particle velocity recorded at the receiver into their up-going and down-going constituents above the seafloor.
Various filters that enable decomposition of seismic data into up-going and down-going constituents have been proposed. For example, K. M. Schalkwijk et al have suggested, in “Application of Two-Step Decomposition to Multi-Component Ocean-Bottom Data: Theory and Case Study”, J. Seism. Expl. Vol. 8 pp261-278 (1999), that the down-going and up-going constituents of the pressure just above the seafloor may be expressed as:
                                                        P              -                        ⁡                          (                              f                ,                k                            )                                =                                                    1                2                            ⁢                              P                ⁡                                  (                                      f                    ,                    k                                    )                                                      -                                          ρ                                  2                  ⁢                                      q                    ⁡                                          (                                              f                        ,                        k                                            )                                                                                  ⁢                                                v                  z                                ⁡                                  (                                      f                    ,                    k                                    )                                                                    ,                                  ⁢                                            P              +                        ⁡                          (                              f                ,                k                            )                                =                                                    1                2                            ⁢              P              ⁢                              (                                  f                  ,                  k                                )                                      +                                          ρ                                  2                  ⁢                                      q                    ⁡                                          (                                              f                        ,                        k                                            )                                                                                  ⁢                                                v                  z                                ⁡                                  (                                      f                    ,                    k                                    )                                                                    ,                            (        1        )            where P is the pressure acquired at the receiver, P− is the up-going constituent of the pressure above the seafloor, P+ is the down-going constituent of the pressure above the seafloor, f is the frequency, k is the horizontal wavenumber, vz is the vertical particle velocity component acquired at the receiver, p is the density of the water, and q is the vertical slowness in the water layer.
As can be seen, the expressions in equation (1) require two of the components of seismic data recorded at the receiver to be combined. These filters are an example where it is necessary to combine two components of the acquired seismic data. It may also be necessary to combine two or more components of the acquired seismic data in order to decompose the acquired seismic data into p-wave and s-wave (pressure-wave and shear-wave) components, or to remove water level multiple events from the seismic data.
One problem in combining different components of the seismic data acquired at a receiver is that the different components of the seismic data may not be correctly calibrated against one another. This is particularly the case where the two components that are being combined are, as in equation (1), the pressure and the vertical particle velocity. There are usually differences in coupling or impulse response between the hydrophone used to acquire the pressure and the geophone used to acquire the vertical particle velocity. It is necessary to calibrate the data for these differences before the pressure and vertical particle velocity can be combined, and this process is known as “P/vz calibration”. This calibration process involves developing a calibration filter that compensates for the differences in coupling and impulse response between the hydrophone and the vertical geophone and then applying the filter to one data set to compensate for the differences in coupling.
Schalkwijk et al, and others, have suggested that the P/vz calibration problem can be addressed by assuming that one component of the seismic data has been correctly recorded, and calibrating the other component of the seismic data against the component that is assumed to be correctly recorded. In general, it is assumed that the hydrophone is well coupled to the seismic wavefield, so that the pressure recording is taken to be correct. The vertical component of the particle velocity is then calibrated against the pressure to compensate for coupling and impulse response differences between the hydrophone and the vertical geophone. Schalkwijk et al therefore proposed that equation (1) above should be modified by applying a calibration filter to the vertical particle velocity. They proposed that the equation given above for the down-going constituent of the pressure above the seafloor should be modified to read as follows:
                                          P            +                    ⁡                      (                          f              ,              k                        )                          =                                            1              2                        ⁢                          P              ⁡                              (                                  f                  ,                  k                                )                                              +                                    a              ⁡                              (                f                )                                      ⁢                          ρ                              2                ⁢                                  q                  ⁡                                      (                                          f                      ,                      k                                        )                                                                        ⁢                                                            v                  z                                ⁡                                  (                                      f                    ,                    k                                    )                                            .                                                          (        2        )            
In equation (2) a(f) represents a frequency-dependent calibration filter. The remaining terms in equation (2) have the same meaning as in equation (1).
The method proposed by Schalkwijk et al. for determining the calibration filter a(f) is to find the calibration filter that minimises the energy of the down-going pressure constituent above the seafloor for a portion of the seismic data that contains only primary reflections. Seismic energy travelling along a primary reflection path is propagating upwardly just above the seafloor at the receiver position, so that the down-going constituent of the pressure just above the seafloor should be zero for a primary reflections. Schalkwijk et al. used a least squares method to find the calibration filter that minimises the energy of the down-going constituent of the pressure in a window containing only primary reflection events. Once the calibration filter a(f) has been determined in this way, it is applied to the entire data set to calibrate the vertical particle velocity.
The existence of various paths of seismic energy from the source to the receiver means that the data acquired at the receiver in a real seismic survey will contain events corresponding to more than one possible path. These events will occur at different times after the actuation of the seismic source 1, as different paths of seismic energy have different associated travel times. In order to apply the method of Schalkwijk et al. to determine the calibration filter, data in a time window that contains only a primary reflection event must be selected.
The method proposed by Schalkwijk et al. has the disadvantage that the time window containing only primary reflection events has to be picked manually. The primary reflection events are not the first events acquired at the receiver following actuation of the source, and so cannot be picked automatically. A further disadvantage is that in some cases, for example if the seismic source has a long signature, it may be hard to distinguish between the direct arrival and the primary reflection events, so that it may be difficult to isolate the correct events. Moreover, in shallow water the water layer multiple events may arrive shortly after the direct wave. In this case, the derivation of a(f) is based on a very limited amount of data, reducing the accuracy of the results. The direct event and water multiple events contain downwardly propagating seismic energy so that use of a time window that inadvertently included the direct event or water multiple events would not give correct results for the calibration filter.
Co-pending UK Patent application No. 0200560.1 and PCT application PCT/GB 03/00052 propose applying the approach of Schalkwijk et al to a time window containing critically refracted waves, which also contain only up-going energy above the seafloor. This technique is more suitable for automation using first-break pickers, and allows the method to be applied to data acquired in shallow waters.
Ball, V. L. and Corrigan, D. suggest, in “Dual sensor summation of noisy ocean-bottom data”, 66th Ann. Internat. Mtg: Soc. of Expl. Geophys., 28-31 (1996), calibrating the vertical geophone data against pressure by applying a hydrophone ghost operator to vz and a geophone ghost operator to the pressure. It can be shown that this approach is equivalent to predicting the down-going pressure reflected from the sea surface from the computed up-going pressure. Minimising the difference between the predicted and the computed down-going pressure reflected from the sea surface at times larger than source duration plus the one-way propagation time through the water layer then allows the desired calibration filter to be determined. A significant drawback of this technique is the need for accurate information about the depth of the water column in the survey area.
Another approach to calibrating data for differences before the pressure and vertical particle velocity is to require seismic energy to be preserved during propagation through the water layer. In this case, frequency- and wavenumber-dependent calibration operators are designed by means of spectral balancing of the up- and down-going wave constituents just above the seafloor.